Statistical Learning TheoryIntroduction: The Problem of Induction and Statistical Inference. Two Approaches to the Learning Problem. Appendix to Chapter1: Methods for Solving III-Posed Problems. Estimation of the Probability Measure and Problem of Learning. Conditions for Consistency of Empirical Risk Minimization Principle. Bounds on the Risk for Indicator Loss Functions. Appendix to Chapter 4: Lower Bounds on the Risk of the ERM Principle. Bounds on the Risk for Real-Valued Loss Functions. The Structural Risk Minimization Principle. Appendix to Chapter 6: Estimating Functions on the Basis of Indirect Measurements. Stochastic III-Posed Problems. Estimating the Values of Function at Given Points. Perceptrons and Their Generalizations. The Support Vector Method for Estimating Indicator Functions. The Support Vector Method for Estimating Real-Valued Functions. SV Machines for Pattern Recognition. SV Machines for Function Approximations, Regression Estimation, and Signal Processing. Necessary and Sufficient Conditions for Uniform Convergence of Frequencies to Their Probabilities. Necessary and Sufficient Conditions for Uniform Convergence of Means to Their Expectations. Necessary and Sufficient Conditions for Uniform One-Sided Convergence of Means to Their Expectations. |
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The Problem of Induction and Statistical | 1 |
0 | 10 |
THEORY OF LEARNING AND GENERALIZATION | 17 |
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algorithm approximation bounded functions Chapter classical coefficients consider constraints construct converges in probability decision rules defined denote density estimation described dF(z distribution function empirical risk functional empirical risk minimization equal equivalence classes exists feature space finite number func given set growth function holds true ill-posed problems indicator functions inequality kernel learning machine lemma linear loss function method metric minimize the functional minimizes the empirical number of elements obtain operator equation optimal hyperplane optimization problem parameters polynomial probability measure Q(zi random variable rate of convergence real-valued functions Remp Remp(a right-hand side risk functional satisfy Section sequence set of functions set of indicator set of real-valued solution solving structural risk minimization structure subset support vectors SV machine Theorem tion training data uniform convergence valid VC dimension zero ΕΛ